Solve for $x$ and $y$ using elimination. $\begin{align*}-5x-3y &= -4 \\ -6x-2y &= -3\end{align*}$
Explanation: We can eliminate $y$ when its corresponding coefficients are negative inverses. Recalling our knowledge of least common multiples, multiply the top equation by $-2$ and the bottom equation by $3$ $\begin{align*}10x+6y &= 8\\ -18x-6y &= -9\end{align*}$ Add the top and bottom equations. $-8x = -1$ Divide both sides by $-8$ and reduce as necessary. $x = \dfrac{1}{8}$ Substitute $\dfrac{1}{8}$ for $x$ in the top equation. $-5( \dfrac{1}{8})-3y = -4$ $-\dfrac{5}{8}-3y = -4$ $-3y = -\dfrac{27}{8}$ $y = \dfrac{9}{8}$ The solution is $\enspace x = \dfrac{1}{8}, \enspace y = \dfrac{9}{8}$.